I recently finished a
series of posts
outlining the basis of quantum field theory. These posts offer a basic and
simplified (albeit not simple) outline of the scientific basis of my work.
It is important to understand them, because everything else that I do builds on that.
In the last of those posts,
I suggested that Quantum physics was broadly consistent with Aristotelian
metaphysics. Not completely consistent, of course: we have to make some
modifications to Aristotle's world-view, most importantly his reluctance
to view physics mathematically (although, to be fair to him, the
mathematics needed to represent causality and space and time is well
beyond what was available in his time, or even the medieval schoolmen who
perfected his system). I don't claim that Aristotle's
philosophy is the end of the discussion, only that it offers a better
beginning for the search for a philosophy consistent with contemporary
physics than the numerous alternatives that arose following the
intellectual revolution that gave birth to Galilean and Newtonian physics.

Yes, but what about all those philosophies that sprung up since the
Aristotelian world-view was originally overthrown? Surely there must be
something of use there as well?

In some cases, yes, to an extent. For example, in my discussion of
mechanism
I highlighted that one triumph of the mechanical philosophy, indeed just
about the only thing it got right, was the idea that physical objects and
concepts such as space and time can and should be treated geometrically
and mathematically. That was a big leap forward, and Aristotle was wrong
to deny that it could or should be done. But there is no doubt that the
majority of the axioms of the mechanical world-view, as it developed and
dominated from the fourteenth through to the nineteenth centuries, is no
longer feasible. An alternative needs to be found.

The
empiricist philosophers,
while wrong to say that their method was the only way we can gain
understanding, nonetheless correctly highlighted the importance of
empirical research; induction from carefully controlled experiments.
They inspired a lot of good work in that regard.
We understand a great deal more now than could have been possible through
induction alone, and have undermined almost all of the empiricists
grandiose claims about their epistemology, but Newtonian and modern
science would not have got going
without the head-start given by those early pioneers of the experimental
method. Aristotle this
time was not completely wrong: he valued observation, but did not
appreciate the systematic and detailed experimentation that was necessary.

Aristotle was right to say that things could not be reduced to the sum of
their parts (i.e. each phenomena ca be reduced to independent parts which
can be studied individually, understood, then stitched back together again
to give an understanding of the whole). Effective Hamiltonians are not
linear sums of the fundamental Hamiltonian; one cannot just take what we
understand about quarks and say that a proton is just three quarks bound
together, and from that alone deduce that the properties of the proton are
just the total properties of the quarks. It's harder than that.
But nonetheless, the idea of the empiricists that one could understand
complex ideas by thinking of them as a collection of various simple ideas
is
a useful first approximation in many systems. It can't get us all the way,
but it can get us started.

But now I come to a view for which there is no merit whatsoever.
No redeeming feature which we can learn from it while building up a
philosophy of quantum physics.
Nominalism. That is easily shown to be inconsistent with contemporary
physics, and must be abandoned.

First of all, some definitions. Nominalism is the belief that there are
no universals or abstract concepts, only physical particulars. The most
important opposing school to nominalism is realism, which states that
there are universals. The other school is conceptionalism, which states
that universals exist, but only in our mental understanding and
classifications, but not in the physical world.

A universal
is basically something which is shared between numerous different objects.
So, for example, two different oak trees share the universal oak.
Perhaps the strongest form of realism, Plato's version, shows the
relationship between the universal and the object in the clearest way.
In Plato's philosophy, the real world is the world of abstract ideas, or
forms. The physical world we see is only secondary, a dim reflection of
that ideal world. Our bodies and senses are limited in that we can only
see the physical world. But our intellect is capable of going beyond it,
and grasping the forms themselves, and walking in the higher existence.

In the world of forms, there is one of each type of being, so there is
a single oak tree. The analogy that Plato used was of a projector passing
light through that real tree onto the physical world. The image appears
numerous times, as it is reflected from different angles.
But the quality of the wall where the projection is made
is slightly different, so the image is slightly distorted in each case,
and distorted in different ways.
Thus we find differences between each physical oak tree. But all of them
are nonetheless originated from that one universal oak, and thus they can
all be said to share in the universal. Clearly, like all pictures, this
has its limitations, and shouldn't be followed too literally. Its most
obvious flaws are limitations of the illustration rather than the
underlying physical idea behind it. The main
idea is that everything in this world is a distorted reflection of that
single individual universal.

Moderate Realism, or Aristotle's realism, takes this in a slightly
different direction. It denies that there is a separate world of forms.
Instead, it states
that the form exists as a part of the various beings that institute it,
or can be instituted in a mind. However it has no independent existence.
I define the form in terms of a set of topologically connected under
infinitesimal deformations effective
Hamiltonians (a more useful definition for physicists than biologists,
but since I'm a physicist I don't care too much about that). From this
effective Hamiltonian, we can derive the structures, arrangements of
matter, and properties of the beings. An ethanol molecule, for example,
is the union between matter and form. When we have two ethanol molecules,
they are distinguished from each other by having different matter, but
they share the same form, in that they are each described by the same
set of effective Hamiltonians.

The nominalist, however, denies all this. He believes that there are
only particular objects with similar properties. The only thing they have
in common is the name we give them on account of those similarities. But
that classification is only an illusion; ultimately there is nothing
connecting the two different molecules.

The history of nominalism is a long one, and it is possibly an older
doctrine than realism. It originally dated back to the ancient Greeks.
However, modern nominalism began in the early middle ages. William of
Ockham and Buridan are often credited as the first Western European
nominalists (perhaps correctly, perhaps they were just pre-cursors who
merely inspired the nominalists). However, it was not until the
Renaissance and early modern period when the doctrine really began to
flourish and dominate. Most later writers that I have seen just assumed
that nominalism was correct, and discounted realism.

For example, Thomas Hobbes wrote,

This universality of one name to many things, hath been the cause that
men think that the things themselves are universal. And do seriously
contend, that besides Peter and John, and all the rest of the men that
are, have been, or shall be in the world, there is yet somewhat else that
we call man, (viz.) man in general, deceiving themselves by taking the
universal, or general appellation, for the thing it signifies. For if one
should desire the painter to make him the picture of a man, which is as
much as to say, of a man in general; he meaneth no more, but that the
painter shall choose what man he pleaseth to draw, which must needs be
some of them that are, have been, or may be, none of which are universal.
But when he would have him to draw the picture of the king, or any
particular person, he limiteth the painter to that one person himself
chooseth. It is plain therefore, that there is nothing universal but
names; which are therefore also called indefinite; because we limit them
not ourselves, but leave them to be applied by the hearer: whereas a
singular name is limited or restrained to one of the many things it
signifieth; as when we say, this man, pointing to him, or giving him
his proper name, or by some such other way.

This argument against realism is easily answered. The realist will argue
that the form doesn't map
to a single state but a set of states. But a picture is a static
image. We can only take pictures of
single states. Therefore we cannot in principle paint a picture of the
form in its entirety, but only one particular exemplification.
Realists accept both individualisation and universals.
Nominalists accept individualisation but deny universals.
That
a painter can paint an individual man demonstrates the principle of
individualisation. But both realists and nominalists accept that. It says
nothing about the existence of
of universals. Both realists and nominalists
deny that they can be painted (albeit for different reasons). Therefore
Hobbes argument says nothing against realism and nothing in favour of
nominalism, but merely reiterates what both sides accept.

Or Hume,

Thirdly, ’tis a principle generally receiv’d in philosophy, that every
thing in nature is individual, and that ’tis utterly absurd to suppose a
triangle really existent, which has no precise proportion of sides and
angles. If this therefore be absurd in fact and reality, it must also be
absurd in idea; since nothing of which we can form a clear and distinct
idea is absurd and impossible. But to form the idea of an object, and to
form an idea simply is the same thing; the reference of the idea to an
object being an extraneous denomination, of which in itself it bears no
mark or character. Now as ’tis impossible to form an idea of an object,
that is possest of quantity and quality, and yet is possest of no precise
degree of either; it follows, that there is an equal impossibility of
forming an idea, that is not limited and confin’d in both these
particulars. Abstract ideas are therefore in themselves individual,
however they may become general in their representation. The image in the
mind is only that of a particular object, tho’ the application of it in
our reasoning be the same, as if it were universal.

So Hume was even worse than Hobbes in his attempt to justify nominalism.
His argument, such as it is, is so dependent on Hume's wider
empiricist philosophy,
that is lacking in so many respects, that it is next to useless.
No realist would say that the universal triangularity can be represented
by a single triangle. No realist would accept Hume's presumption that the
only way to understand something is to visualise it (to form an idea, in
Hume's terminology). And even if we do so, the universal triangularity
would correspond to a set of imaginable triangles rather than an individual
one (but in reality, it is not the set of states, but the underlying
principle that unites them). Hume's argument is basically to assume that
we have to think of universals in the same way that we think of particulars,
say that universals can't be thought of as particulars, and conclude that
there are no universals. A realist would never accept that first
assumption, nor the empiricist "reasoning" used to support it.

So are there any good arguments out there for nominalism? I think that
there were, when physics was less advanced.

Nominalism arises naturally from the mechanical philosophy and mechanical
physics combined with the atomic principle. For if everything can be
reduced to the sum of its parts (as mechanism supposes) and those parts
are a small number of corpuscles, with differences arising from different
arrangements of those fundamental particles (as the atomic principle
supposes), then objects may be similar in structure merely coincidentally.
Newton's laws don't care whether it is one type of particle or another;
they act on all matter in the same way. There is no mention of universals
in Newtonian physics. All there is is matter, some of which
superficially resembles others. If we were to take electrons and took them
into classical physics, they would merely be two different particles with
a similar mass and charge. Nothing in physics would depend on them both
being the same type of particle. There is no reason why they should have
the same mass; it is just a coincidence. Thus we can easily claim that the
universal "electron" is redundant. If redundant, we may as well omit it,
which leads us to nominalism, at least in this regard.

But now we come to quantum physics. Immediately we see a difference.
For now each electron is merely a single excitation of a single universal
electron field. The mass of an electron is determined by the coupling
of that universal field to
the scalar field in the standard model; the electric charge by the coupling
to the photon field. All electrons arise from the same field, so they
each have the same couplings, not by coincidence but by logical necessity.

That alone would seem to suggest the existence of a universal that
describes electrons. The whole basis of quantum field theory is that
it makes universals, namely the quantum fields themselves, its chief players.
But there is more.

One of the most important results in quantum physics is the Pauli
exclusion principle. This states that two fermions of the same type
cannot be in the same state at the same time. It is why a lithium atom
cannot have three electrons in its lowest energy level, but only one
spin up and one spin down electron. The next electron must jump to the
next highest level. That's why the different chemical elements have their
different properties.

Ultimately, the exclusion principle arises from the commutation or
anti-commutation relationships between the creation operators for the
fields. Although you can pile as many Bosons into the same state as you
like, that they are the same type of particle still affects the physics.
In other words, the fundamental particles of nature come in distinct types,
and this leads to clear experimental consequences.

My favourite example of this is the scattering experiment. We can fire two
electrons towards each other, they "bounce" off each other, and we measure
the angular distribution of the result. The final result of this
experiment depends on whether the two particles are of the same type.
For example, scatter two electrons, or two muons, and one would get a very
different result than if one would scatter a muon against an electron, far
more than we expect from the small difference in mass between the two
particles. For example, we can perform the experiment at increasingly high
energies, where the rest mass of the particles becomes less and less
significant, but the dramatic difference will remain. This occurs because
physics recognises that the two electrons are the same type of particle.
For Bosons, the number of particles hitting the detector at right angles
to the particle beams is twice what you would expect if the particles were
from different fields. For Fermions, it is zero if they are the same type
of particle, and non-zero otherwise.

Nature can recognise whether or not two particles are the same type,
and the scattering distribution is adjusted accordingly.
So types exist in nature, at least at the level of fundamental particles,
and types are a kind of universal. Thus at the level of fundamental, physics
nominalism is wrong. Realism and Nominalism have experimental consequences,
and the experiments come out in favour of realism.

But if we accept realism at the most fundamental
layer of physics, then we must also accept it at the next layer. We
can construct the creation operator for the proton from the
creation operators of the quarks and gluons. It is not simply a linear
addition (as mechanism would suppose), but it nonetheless can be done
in a systematic way that is the same for each proton. Thus the universal
of quarks leads to the idea of the universal of protons. We can extend
realism to the first layer of composite particles. From this, we can go to
the next layer, and so on up the chain of physics and chemistry.

Nominalism states that there are no universals. Thanks to physics, we
know that there are. Therefore nominalism is false. The question is
whether there is anything that can be rescued for the philosophy. Any
area of study separate from everything else where we can apply nominalist
reasoning.

I admit that disproving nominalism in biology is a bit more of an issue
in this construction. Here the
universal is not one of identity but of resemblance. But by going back
to the DNA sequence, and looking for infinitesimal changes between viable
individuals we can circle off different species. Again, we have universals.
Nominalism with regards to objects is false.

So far, I have just discussed nominalism in terms of universals of
physical objects. Of course, there are also said to be universals of
properties or observables. Realists say that there is a universal
red. Nominalists
deny this and say that the colours are only coincidentally similar. I
personally dislike the fixation on such properties or predicates by
philosophers. Firstly, one cannot generalise so easily. The physics of
colour is very different from the physics of texture and so on, and to
lump them all under the same category of predicate is misleading.
Secondly, the form, or substance itself, is primary, and properties
secondary. Many modern philosophers have made the mistake of thinking that
that properties (what we directly sense) are more important to the nature
of the being than the underlying abstract or mathematical form (what
ultimately determines what something is).
But it is the form we encounter first in a physical construction from
first principles.
Form is determined from the Hamiltonian, which is put together from the
creation operators of the particles, which are fundamental.
The properties are derived from the Hamiltonian,
for example colour from the gaps in the energy bands of a substance.
(We are, of course, in the nominalism against realism debate always
speaking of colour as a property of an object rather
than the interpretation of that as an image in our mind. They are two
different definitions of the term, and should not be confused). And this gives
us our answer regarding property realism. We have a universal regarding
a particular paint pigment (the object). Everything that is derived from
a universal must itself be a universal. From the universal form we
derive the universal energy bands, and from those the universal of colour.
The same for any other property. Thus we must be property realists as well
as object realists.

A lot, not all but a lot, of modern philosophy takes Nominalism as one
of its axioms. Some major philosophers made the mistake of establishing it
as a basic principle, so much so that all their theories wholly depend on it.
This means that a lot of what is taught in modern philosophy departments
is directly contradicted by contemporary physics. And in any
genuine disagreement, the philosophers must bow to the physicists,
who have experiment to guide them. A great many of modern philosophers
spend a great deal of time pondering over the details of theories that
have been firmly disproved.

So the only remaining debate is not nominalism against realism, but which
type of realism should we adopt.

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